1207.2751 (Dana Fine et al.)

Supersymmetic Quantum Mechanics and the Gauss-Bonnet-Chern Theorem    [PDF]

Dana Fine, Stephen Sawin

Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products of the approximate short-time propagator over a partition of a finite time interval. This limit is shown to converge uniformly for finite time as kernels, and to admit a version of steepest descent approximation sufficiently robust that the path integral "proof" of the Gauss-Bonnet-Chern Theorem becomes directly rigorous.

View original: http://arxiv.org/abs/1207.2751